Some welding operations require a welding torch to be oscillated about an axis while also being moved vertically, forwardly or rearwardly, and laterally. In my U.S. Pat. No. 3,970,232, a welding machine is disclosed which provides cam-controlled oscillation of a welding torch about a generally-vertical axis while also providing cam-controlled forward-rearward movement of that torch. The welding machine of that patent is very useful and successful, but it does not provide vertical movement of the torch relative to the workpiece, and it also does not provide cam-controlled lateral movement of that torch. My co-pending application Ser. No. 19,764, which was filed on Mar. 12, 1979 for a WELDING MACHINE and which issued as U.S. Pat. No. 4,248,371, discloses cam-controlled oscillation of a welding torch about a generally-vertical axis and cam-controlled up-down and forward-rearward movement of that torch. The welding machine of said application is very useful and successful; but the forward-rearward movement is arcuate rather than linear, and the up-down movement is along an axis which tilts relative to the vertical. As a result, the designing of cams for different workpieces requires the designer to compensate for the non-linear forward-rearward movement and for the non-vertical up-down movement of the welding torch. Also, that application does not disclose cam-controlled lateral movement of the welding torch.